Diffusion-Controlled Spherulite Growth in Obsidian Inferred from H2O Concentration Proﬁles

Contrib Mineral Petrol DOI 10.1007/s00410-008-0327-8

ORIGINAL PAPER

Diffusion-controlled spherulite growth in obsidian inferred from H2O concentration proﬁles

Jim Watkins Æ Michael Manga Æ Christian Huber Æ Michael Martin

Received: 3 November 2007 / Accepted: 8 July 2008 Ó Springer-Verlag 2008

Abstract Spherulites are spherical clusters of radiating Keywords Spherulites Obsidian FTIR crystals that occur naturally in rhyolitic obsidian. The Advection–diffusion growth of spherulites requires diffusion and uptake of crystal forming components from the host rhyolite melt or glass, and rejection of non-crystal forming components Introduction from the crystallizing region. Water concentration profiles measured by synchrotron-source Fourier transform spec- Spherulites are polycrystalline solids that develop under troscopy reveal that water is expelled into the surrounding highly non-equilibrium conditions in liquids (Keith and matrix during spherulite growth, and that it diffuses out- Padden 1963). Natural spherulites are commonly found in ward ahead of the advancing crystalline front. We compare rhyolitic obsidian and have evoked the curiosity of petrol- these profiles to models of water diffusion in rhyolite to ogists for more than a century (e.g., Judd 1888; Cross 1891). estimate timescales for spherulite growth. Using a diffu- Over the past several decades, numerous studies on spher- sion-controlled growth law, we find that spherulites can ulite morphology (Keith and Padden 1964a; Lofgren grow on the order of days to months at temperatures above 1971a), kinetics of spherulite growth (Keith and Padden the glass transition. The diffusion-controlled growth law 1964b; Lofgren 1971b), disequilibrium crystal growth rates also accounts for spherulite size distribution, spherulite and textures (Fenn 1977; Swanson 1977), and field obser- growth below the glass transition, and why spherulitic vations (Mittwede 1988; Swanson et al. 1989; Manley and glasses are not completely devitrified. Fink 1987; Manley 1992; Davis and McPhie 1996; Mac- Arthur et al. 1998, and many others) have shed light on the conditions and processes behind spherulite nucleation and Communicated by J. Blundy. growth. Despite the long-standing interest, several funda- mental questions persist. For example: On what timescales J. Watkins (&) M. Manga C. Huber do natural spherulites form? At what degree of undercooling Department of Earth and Planetary Science, do spherulites begin to grow? Can spherulites grow below University of California, Berkeley, CA, USA the glass transition? Why doesn’t spherulite growth lead to e-mail: [email protected] runaway heating? And, why are spherulites spherical? In M. Manga this paper, we revisit these questions and contribute a new e-mail: [email protected] quantitative approach for estimating spherulite growth rates.

C. Huber e-mail: [email protected] Qualitative description of spherulite growth M. Martin Advanced Light Source, Spherulites in rhyolitic obsidian are composed primarily of Lawrence Berkeley National Laboratory, Berkeley, CA, USA alkali feldspar and SiO2 polymorphs. Spherulites are often e-mail: [email protected] mm-scale, but are known to range from submicroscopic to 123 Contrib Mineral Petrol m-scale (e.g., Smith et al. 2001). They may be randomly Tequila volcanic field, western Mexico. Lavas that range in distributed and completely isolated, or nucleate preferen- composition from basalt to rhyolite surround an andesite tially to form clusters or trains (e.g., Davis and McPhie stratovolcano (Volcań Tequila) that formed about 200 kyr 1996). Within a deposit, spherulitic textures and relation- ago (Lewis-Kenedi et al. 2005). The rhyolites and obsidian ships may vary widely owing to local differences in domes are among the earliest erupted units, ranging in age emplacement temperature, flow depth, cooling rate, and from 0.23 to 1.0 Ma (Lewis-Kenedi et al. 2005). surface hydrology (Manley 1992; MacArthur et al. 1998). Figure 1 is a photograph of the obsidian hand sample Despite these complexities, the fact that spherulites occur used in this study. The matrix is a dark, coherent glass that almost exclusively in glasses seems to require conditions has not undergone post-magmatic hydration. It contains that yield slow nucleation rates yet relatively rapid crystal some visible but subtle ‘‘flow bands’’ reflecting shear flow growth rates. of magmatic parcels containing variable microlite content

As a melt cools below the liquidus temperature (Teq) for (Gonnermann and Manga 2003). Isolated, light grey a given crystalline phase, an energy barrier must be over- spherulites cross-cut flow bands and exhibit a range of come in order for the new phase to nucleate and grow. Just sizes that are distributed homogeneously (Fig. 1). below Teq, this energy barrier is finite and decreases with Individual spherulites are host to three crystalline pha- decreasing temperature. A certain amount of undercooling ses: 55–65% (by volume) feldspar fibers, *30–40% oblate is always necessary to nucleate a solid phase (Carmichael cristobalite masses, and \1% Fe- and Ti-oxides. The et al. 1974), where the degree of undercooling (DT) is the feldspar fibers are arranged in a radial habit about a central difference between the equilibrium temperature Teq and the nucleus and are enclosed by the cristobalite masses. X-ray actual magmatic temperature T. In siliceous lavas, atomic diffraction patterns indicate the feldspar is some form of mobility is sluggish and large DT can be achieved prior to alkali feldspar, but an exact determination could not be nucleation. Once nucleation does occur, crystal growth made. There is also a significant amount of void space due proceeds and crystal growth rates are dictated by the to the *10% volume contraction associated with crystal- magnitude of DT. lization, which we neglect in our calculations. Large undercoolings promote rapid crystallization, but are also associated with lower magmatic temperatures and slower elemental diffusivities. For crystals growing from a Sample preparation and measurements melt or glass of different composition, crystal growth rates are limited by the ability of melt components to diffuse Four rectangular billets (*21 mm 9 38 mm) of spheru- towards or away from the crystallizing front. In the case of litic obsidian were cut from a hand sample (Fig. 1)tobe spherulites, it is has been shown that certain major- and trace- prepared for FTIR analysis. Each billet was ground down elements are rejected by crystallizing phases and concen- until at least one spherulite was sectioned through its trated at the spherulite–glass interface (Smith et al. 2001). center. The surface with the spherulite was polished to Since the mineral phases that compose rhyolitic *0.25 lm. The polished surface was mounted on a glass spherulites are nominally anhydrous, water is also rejected slide with epoxy and the billet was cut to a thickness of from the crystalline region. Among incompatible melt *300 lm. The grinding and polishing procedure was species, water is perhaps the most extensively studied repeated on the opposite surface to obtain a doubly pol- because of its pronounced effects on magma viscosity and ished wafer. Each of the samples was of uniform thickness major-element diffusion coefficients. As a result, methods (±\5% as determined by a digital micrometer with a for determining water concentrations in rhyolitic glasses precision of ±2 lm) so that infrared absorption data could have been developed over the past 25 years (e.g., Stolper be compared throughout the sample. Polished surfaces 1982; Newman et al. 1986, Zhang et al. 1997) using Fou- were necessary for minimizing infrared scattering and rier transform infrared spectroscopy (FTIR). The goal of obtaining quality absorbance data. our measurements is to use FTIR to resolve water con- Water concentration measurements were made by syn- centration gradients at the spherulite–glass interface with chrotron-source FTIR at the Advanced Light Source at high spatial resolution (see Castro et al. 2005) to better Lawrence Berkeley National Laboratory. The instrument understand the growth history of spherulites. used was a Nicolet 760 FTIR spectrometer interfaced with a Spectra-Tech Nic-Plan IR microscope capable of spot sizes of 3–10 lm (Martin and McKinney 1998). Transects Sample descriptions were oriented perpendicular to spherulite rims and measurements were made on the surrounding glassy matrix. The spherulites analyzed in this study are from a hand Total water concentrations were determined from the sample of a rhyolitic vitrophyre that lies in the Quaternary intensity of the 3,570 cm-1 peak (Newman et al. 1986), 123 Contrib Mineral Petrol

Fig. 1 a Photograph of a spherulitic obsidian from b) Tequila volcano. Spherulites ranging in size from 1.0 to 8.0 mm in diameter are a) distributed homogeneously throughout. b Cathodilluminescence image showing ﬁbrous alkali-feldspar crystals enclosed by oblate 100 µm cristobalite masses within an individual spherulite. c Thin section image showing spherulites cross-cutting subtle ﬂow bands c)

5 mm

5 cm which reflects the abundance of hydrous species (XOH) elements could not be resolved quantitatively within including molecular water (HOH). Hereafter, we refer to detection limits. However, qualitative variations are all hydrous species collectively as ‘‘water’’. Analytical resolved through detailed WDS X-ray mapping for three error is estimated to be ±0.005 wt% based on repeated major elements taken on an individual spherulite (Fig. 3). measurements. A close look at the rim–matrix interface reveals a relative Figure 2 shows data from a transect between two adja- depletion in crystallizing components K and Si and con- cent spherulites. At the rim–matrix interface of each comitant enrichment in Na. spherulite, there is a local maximum in water content that decreases with distance into the surrounding matrix to Interpretation background levels (*0.115 wt% in this case). Similar profiles were measured on seven spherulites ranging in size Spherulite growth from a liquid or glass of different from 1.7 to 5.2 mm in diameter. composition requires diffusion of crystal-forming compo- One of the samples was also analyzed using a Cameca nents, which become depleted over diffusive lengthscales SX-51 electron microprobe to characterize major-element around the crystallizing region. Figures 2 and 3 clearly variations. Due to the similarity in bulk composition illustrate this process and confirm that impurities are not between spherulites and their host, gradients in major trapped within crystals or interstitial voids. The outward rejection of water induces a concentration gradient down which water diffuses into the surrounding matrix, resulting 0.20 Spherulite rim in profiles like that shown in Fig. 2. Spherulite rim For four of the seven spherulites analyzed, the data were clean enough to demonstrate that [95% of the water from 0.15 the volume occupied by the spherulite could be accounted for in the water diffusion profile. This is noteworthy because it provides a stoichiometric relationship between 0.10 the moles of water removed and moles of sanidine (or Obsidian glass cristobalite) crystallized within the spherulite volume, thus O content (wt. %) 2 allowing water rejection and diffusion to be used as a proxy H 0.05 for spherulite growth.

0 0 1 2 3 4 5 6 7 Model for spherulite growth Distance (mm) With each increment of spherulite growth, a known Fig. 2 FTIR transect between two spherulites of different size illustrating the expulsion of water into the surrounding melt or glass amount of water is expelled ahead of the advancing during spherulite growth crystalline front. In this way, water diffusion into the 123 Contrib Mineral Petrol

Fig. 3 Cathodilluminescence image of a spherulite (upper left) and electron microprobe element maps on the same spherulite. Dark regions correspond to relatively low concentrations. Note the relative enrichment in Na and depletion in K and Si at the spherulite boundary

matrix is in competition with the propagating spherulite ur ¼ n DOH ð3Þ boundary. Here we present a model that tracks the expulsion and diffusion of water during spherulite growth where n is a free parameter that represents the competition in the reference frame of the expanding spherulite rim. In between spherulite growth and water diffusion. this reference frame, the profiles in Fig. 3 can be mod- A possible alternative is a diffusion-controlled growth law (Granasy et al. 2005), whereby the radius scales with eled by solving numerically the advection–diffusion 1/2 equation: time as t : 1=2 oC DOH u rC ¼r½D rC ð1Þ ur ¼ a ð4Þ ot OH t where C is the concentration of water, u is the velocity of where a is a free parameter analogous to n in the linear the growing interface, and DOH(C,T,P) is the diffusivity of case. water in rhyolite melt or glass. Zhang and Behrens (2000) The appropriate boundary conditions for this problem showed that DOH(C,T,P) varies linearly with water are: (1) fixed concentration of water far from the growing concentration at low total water contents (less than about interface and (2) time-dependent concentration of water at 2 wt%), and we account for this effect in our model. the rim–matrix interface that is related to the flux of water

However, we do not include variations in DOH(C,T,P) with expelled during each increment of growth. The second temperature and pressure—a simplifying assumption boundary condition is implemented by ensuring mass discussed later. Taking advantage of the spherical conservation: symmetry of spherulites, (1) can be simpliﬁed and ZR1 1 expressed as a function of the radial distance only: ðÞCðr; tÞC r2dr ¼ C RðtÞ3 ð5Þ 1 3 1 oC oC RðtÞ o ur o ¼ DOHðÞr ð2Þ t r where C(r,t) is the concentration of water at a distance r from where DOH is updated at the beginning of each timestep. the center of the spherulite, R is the spherulite radius, and C1 The velocity of the interface ur (ur = dR/dt where R is represents the background concentration of water at some the radius of the spherulite) is given by the choice of distance R1 into the surrounding matrix. Equation (5) states spherulite growth law. Keith and Padden (1963) found that the water represented under the diffusion proﬁle is equal experimentally that at constant temperature, spherulites in to 100% of the water that once occupied the spherulite vol- polymer liquids generally grow according to a linear ume. Any difference between these two values is used to growth law whereby ur is constant and R scales with update C(R,t) after each timestep so that the equality is true. time as t: Figure 4 is a schematic illustration of the model setup.

123 Contrib Mineral Petrol

Cwater ur C Spherulite water, initial Water concentration Water

r 0 r=R r=R+dR

Fig. 4 Schematic diagram summarizing the 1D spherulite growth represents an increase in spherulite radius from R to R + dR, and the and water diffusion model. The dark black line represents actual water within this region is removed and ﬂuxed into the new boundary (time-dependent) water concentration and dashed line represents the at R + dR. The model assumes perfectly efﬁcient water expulsion initial water concentration. The width of the vertical gray bar

Results linear growth whereas the figures on the right (Fig. 6b, d) assume diffusion-controlled growth. Although the agree- The temporal evolution of model water concentration ment between model curves and measured profiles is not profiles depends strongly on the choice of growth law. very satisfying, it is clear that an equally good (or, for that Figure 5 compares model profiles using both the linear matter, equally poor) fit can be achieved using either growth law (5a) and the diffusion-controlled growth law growth law for a given spherulite. However, there is one (5b) as a function of spherulite radius (i.e., time). In the important distinction between the two growth models. linear regime, the concentration of water at the growing Figure 6a, c shows that a smaller coefficient n is required spherulite boundary increases progressively with time. This in going from the smaller to the larger spherulite. In con- is a consequence of the spherical geometry, wherein the trast, Fig. 6b, d shows that a larger coefficient a is required volume of water expelled increases with each (constant) in going from the smaller spherulite to the larger spherulite. growth increment dR. By contrast, in the diffusion-con- The significance of this is discussed in the next section. trolled regime the diffusion of water counterbalances the A striking feature of all measured water concentration time-dependent growth increment dR such that the con- profiles is the ‘‘flattening’’ they exhibit near the rim–matrix centration of water at the spherulite boundary remains interface, which may be attributed to post-growth diffusion relatively constant with time. of water. In order to account for this effect, we use the bold Figure 6 compares model results to measured profiles profiles from Fig. 6 as the initial condition for the post- from two spherulites of different size. The two profiles are growth model, and, as dR/dt = 0, (2) reduces to the dif- representative of those measured in this study and include fusion equation with no-flux boundary conditions (i.e., the largest and smallest spherulites examined. Figure 6a, b water is not allowed to diffuse back into the spherulite). corresponds to data from a spherulite of radius 0.86 mm, Results are summarized in Fig. 7 for the small and large while Fig. 6c, d correspond to data from a spherulite of spherulite. The duration of post-growth diffusion (in years) radius 2.6 mm. The figures on the left (Fig. 6a, c) assume depends on DOH (i.e., temperature), and the values quoted

1.1 0.24

1 a) b) 0.22 0.9

0.8 0.2 0.7

0.6 0.18

0.5

O content (wt. %) O content (wt. %) R=2.6mm 2 2 0.16

H 0.4 R=2.6mm H

0.3 1.0 1.0 0.14 0.5 0.5 0.2 0.3 0.3 0.1 0.12 0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.5 1 1.5 2 2.5 3 Distance (mm) Distance (mm)

Fig. 5 Model calculations showing the evolution of water concen- build-up of water at the edge of the spherulite whereas the diffusion- tration away from spherulite boundaries assuming two different controlled growth law (5b) leads to wider proﬁles and nearly steady spherulite growth laws. Note the different scales for the x- and y-axes. values of water concentration at the spherulite edge The linear growth law (5a) leads to narrow proﬁles with a progressive

123 Contrib Mineral Petrol

0.155 0.155 Measured Measured 0.15 0.15 n=0.0068 a=0.9 1/2 u=n DOH u=a (DOH/t) 0.145 0.145 0.8 0.0052 0.14 Small spherulite (R=0.86mm)0.14 Small spherulite (R=0.86mm)

0.135 0.135 0.7

0.13 0.13 0.0038 0.125 0.125 O content (wt. %) O content (wt. %) 2 2 H H 0.12 0.12

0.115 0.115 a) b) 0.11 0.11 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Distance (mm) Distance (mm)

0.21 0.21 Measured 0.2 n=0.0035 Measured 0.2 a=1.1 u=a (D /t)1/2 u=n DOH OH 0.19 0.19 0.0026 1.02 0.18 0.18 Large spherulite (R=2.60mm) Large spherulite (R=2.60mm) 0.17 0.17 0.9 0.0020 0.16 0.16

0.15 0.15 O content (wt. %) O content (wt. %) 2 0.14 2 0.14 H H 0.13 0.13 0.12 c) 0.12 d) 0.11 0.11 0 0.5 1 1.5 2 2.5 3 0 0.5 1 1.5 2 2.5 3 Distance (mm) Distance (mm)

1/2 Fig. 6 Comparison between measured water concentration proﬁles growth law (i.e., u * (DOH/t) ). Clearly, indistinguishable results and model calculations. a and c show results for two different can be obtained using either growth law for a spherulite of given spherulites using a linear growth law (i.e., u * DOHt). b and d show radius. Dark curves represent initial conditions for post-growth results for two different spherulites using a diffusion-controlled diffusion (see text), which leads to the proﬁles in Fig. 7

0.155 0.21 a)Measured b) Measured 0.15 x years 0.2 x years 0.19 0.145 1 0.18 x=4 0.14 1 Small spherulite (R=0.86mm)7 Large spherulite (R=2.60mm) x=4 0.17 0.135 0.16 7 0.13 0.15 O content (wt. %)

0.125 O content (wt. %) 2 2 0.14 H H 0.12 0.13

0.115 0.12

0.11 0.11 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 0.5 1 1.5 2 2.5 3 Distance (mm) Distance (mm)

Fig. 7 Data versus model profiles after post-growth diffusion of same duration of post-growth diffusion is required to fit profiles for water is included. Initial conditions are bold profiles in Fig. 6. The both large and small spherulites, which is expected assuming a timescales correspond to the lower bound of the experimentally common closure temperature for spherulites from a given locality determined DOH (i.e., T = 400°C; Zhang and Behrens 2000). The in Fig. 7 arbitrarily assume T = 400°C. A lower tempera- Discussion ture would simply require more prolonged post-growth diffusion in order to achieve an identical fit. The two most The distinction between linear and diffusion-controlled important points that arise from Fig. 7 are: (1) the agree- growth laws is important as it pertains to several questions ment between measured and model profiles is markedly presented earlier about natural spherulites. Keith and improved with inclusion of post-growth diffusion, and (2) Padden (1964b) studied spherulite growth kinetics under the same duration of post-growth diffusion is required to fit isothermal conditions in a range of polymer liquids and profiles for both large and small spherulites. found that impurities often become trapped in the

123 Contrib Mineral Petrol interstices of the crystalline region. Under these circum- Diffusion-controlled growth also has implications for stances, impurities do not influence subsequent crystal the size distribution of spherulites. For instance, we should growth and spherulite growth rates are linear in time (Keith expect a greater abundance of larger spherulites because and Padden 1964b). However, the linear growth law breaks rapid initial growth allows smaller spherulites to catch up down when rejected species are sufficiently mobile. That in size to those earlier-forming, larger spherulites. Quali- is, when diffusion of impurities occurs on the same time- tatively, this seems to be the case for our samples. scale as crystal growth rates, the concentration of However, no attempt was made to statistically analyze impurities at the crystalline interface increases progres- spherulite sizes because of the limited size of our hand sively. As a consequence, spherulite growth rates decrease sample and the challenge of sectioning spherulites through with spherulite size owing to the reduction in local con- their center. centrations of crystallizing components. Hence, we interpret the observation of rejected impurities outside the On what timescales do natural spherulites form? crystalline volume as evidence in itself for nonlinear growth kinetics. As discussed by Keith and Padden Using water rejection as a proxy for crystallization rates, it (1964b), the onset of nonlinear growth is favored by is possible to calculate timescales for spherulite growth. reducing the molecular weight of the impurity or by This requires knowledge of the diffusivity of water (DOH) increasing the crystallization temperature to reduce the during spherulite formation, and one obvious shortcoming driving force for crystallization and to enhance impurity of the model is the assumption that DOH is fixed in a diffusivities. Water, the impurity of interest for natural rhyolite undergoing cooling. Nevertheless, we calculate spherulites, satisfies these conditions: it is relatively isothermal spherulite growth rates to bracket the true mobile, depresses the rhyolite liquidus, and enhances the timescales for spherulite formation. Using DOH in rhyolite diffusivity of other melt components. at conditions relevant to our samples (*0.1 wt% water and An additional argument can be made for diffusion- 0.1 MPa; Zhang and Behrens 2000), the time required to controlled growth from the results presented in Figs. 6 and grow a spherulite of given radius comes from the scaling 7. The model curves in Fig. 7 indicate that both spherulites relationship experienced the same duration of post-growth diffusion of R2 water, and hence, stopped growing at the same time or t ð6Þ D temperature. Intuitively, one would expect that the larger OH spherulite began growing earlier at higher temperatures—a where R is the final radius of the spherulite. Results are possibility that is not explicitly accounted for in our model. summarized in Fig. 8, which shows the time required for a

Note, however, that we assume constant a, n, and DOH (constant with respect to temperature). Of these parame- 1e+06 ters, D is the only one that is likely to change with 'dtr3.txt' using 1:2 OH Age of obsidian 'dtr3.txt' using 1:3 100000 'dtr3.txt' using 1:4 temperature during spherulite growth. The observed dif- 'dtr3.txt' using 1:5 200 C 'dtr3.txt' using 1:6 ferences in a and n between spherulites may thus represent 10000 changes in DOH with temperature. In the diffusion-con- 1000 trolled growth model, a larger a translates into a higher 400 C 100 average DOH (i.e., temperature) for the larger spherulite (a = 1.02) versus the smaller spherulite (a = 0.8), con- 10 600 C 800 C time (years) 1 sistent with the expectation stated above. In contrast, if we 1000 C assume a linear growth law, comparable ﬁts between the 0.1 larger spherulite (n = 0.0026) and smaller spherulite 0.01

(n = 0.0052) correspond to lower temperatures (i.e., 0.001 slower average growth rate) for the larger spherulite, which 0.0001 is difficult to reconcile with the assumption that both 0 0.5 1 1.5 2 2.5 3 3.5 4 spherulites stopped growing at the same temperature. Radius (mm) Indeed, using a slightly different modeling approach, Fig. 8 Time required to grow a spherulite of given radius at various Castro et al. (2008) found that larger spherulites experi- fixed temperatures assuming a diffusion-controlled growth law (6) enced higher average growth rates than smaller spherulites. and using a proportionality constant of a = 1.0. The shaded region at In their paper, however, this result was attributed to size- the top of the graph encompasses the range of possible ages for the host obsidian (Lewis-Kenedi et al. 2005) and the dashed line indicates dependent growth rates versus our suggestion here that this the size of the largest spherulite analyzed in this study. For spherulites reflects different temperature histories (i.e., temperature- to grow appreciably on cooling timescales, they must form at dependent growth rates). temperatures above about 400°C 123 Contrib Mineral Petrol spherulite to reach a given radius at various fixed temper- Do spherulites grow below the glass transition? atures. For simplicity, these calculations assume that DOH is not dependent on water concentration. We justify this by The glass transition signals an abrupt change in the phys- noting that these values are within a factor of 2 to the ical properties of a melt, namely a change from liquid-like values we calculate from our full advection–diffusion to solid-like behavior. The temperature at which this takes model for radii greater than about 1 mm. place depends on composition and cooling rate. For

According to the diffusion-controlled growth model, a anhydrous rhyolite, the glass transition temperature (Tg) spherulite of 2.6 mm requires *300 days at 800°C, lies somewhere between 620 and 750°C (based on values *10 years at 600°C, or *300 years at 400°C. These in Swanson et al. 1989; Manley 1992; Westrich et al. timescales are consistent with spherulites forming at tem- 1988), and it has been suggested that Tg may provide a peratures above 600°C in parts of lava flows that cool on minimum temperature for spherulite growth (Ryan and the order of years to decades in heat flow models that Sammis 1981; Manley 1992; Davis and McPhie 1996). assume instantaneous emplacement of lava followed by Indeed, certain field observations such as deformation of static cooling (Manley 1992; Manley and Fink 1987). At spherulites (Mittwede 1988), boudinage of flow bands by temperatures below about 400°C, diffusion-controlled spherulites (Manley 1992; Stevenson et al. 1994), and growth is extremely sluggish and we consider T = 400°C inflation of lithophysal cavities (Swanson et al. 1989) an approximate lower bound for spherulite growth during suggest that spherulite growth takes place in melts above cooling. This can explain the absence of macroscopic Tg. However, these features are not always observed. The spherulites along quench margins where rapid cooling has spherulites used in this study, for instance, are underformed minimized the duration of high temperature growth rates. and cross cut flow bands, raising the possibility that they Of course, better estimates for timescales of spherulite grew, at least in part, below the glass transition. growth require additional constraints on the temperature of Since we assume that spherulite growth is governed by spherulite formation and the cooling history of their host. diffusion of components across spherulite boundaries, the

question of whether spherulites grow below Tg is really a At what degree of undercooling do spherulites question of how elemental diffusivities are affected by the begin to grow? glass transition. Based on the study by Zhang and Behrens (2000), the diffusivity of water appears to vary smoothly Emplacement temperatures for rhyolite vary considerably across the glass transition. Figure 9 shows diffusivities for (790–925°C; Carmichael et al. 1974). At the time of other various chemical species in rhyolitic obsidian as a emplacement, an anhydrous rhyolite lava may be signifi- function of temperature. Across the range of possible glass cantly undercooled, as the liquidus in this system is transition temperatures, there is no evidence for significant *1,000°C (Ghiorso and Sack 1995). Owing to nucleation lag times, which may be on the order of tens of years T ( C) 1000Tg 500 400 300 200 100 (Manley 1992), the degree of undercooling at which -3 'dobs.txt' using 2:3 'dobs.txt' using 2:4 nucleation actually occurs is difficult to constrain. Never- -4 'dobs.txt' using 2:5 'dobs.txt' using 2:6 'dobs.txt' using 2:7 theless, textural relationships can provide a first-order -5 'dobs.txt' using 2:8 'dobs.txt' using 2:9 estimate. For example, crystal morphologies have been H2O 'dobs.txt' using 2:10 -6 He /s) shown to correlate with the degree of undercooling in the 2 -7 NaAlSi O –KAlSi O H O system (Fenn 1977). Feldspars 24Na 3 8 3 8 2 -8 grown in this system formed as (1) isolated tabular crystals -9 8686Rb 42K at low undercoolings (DT \ 40°C), (2) coarse, open log D (mm H O -10 2 spherulites at moderate undercoolings (DT * 75–145°C), 85Sr and (3) fine, closed spherulites at higher undercoolings -11 (DT * 245–395°C) (Fenn 1977). This latter group of -12 H2O textures corresponds to the spherulites pictured in Fig. 1. -13 -14 From this information, a minimum DT on the order of 5 10 15 20 25 30 4 150°C (corresponding to a maximum T = 850°C) seems 10 /T reasonable for the onset of spherulite growth, providing a Fig 9 Temperature-dependence of diffusivities for various chemical minimum growth time of *100 days. Larger DT associ- species in obsidian. Dark line for H2O is from Eq. (12) in Zhang and ated with longer nucleation lag times are certainly possible Behrens (2000) and grey lines for H2O are from obsidian hydration and are probably common given that spherulites are gen- experiments (see Freer 1981). All other lines are from the compilation by Freer (1981). The main point is that major- and trace-element erally smaller than the cooling timescales of decades would diffusivities appear to be insensitive to the glass transition in melts of otherwise allow. rhyolitic composition (region shown in grey) 123 Contrib Mineral Petrol changes in the diffusivity mechanisms for any of the (i.e., higher undercooling) and respond by growing faster. components shown. This is consistent with the notion that This runaway effect can lead to dendritic crystals or rhyolite liquids are structurally similar to rhyolite glasses, ‘‘cellular’’ morphologies (Kirkpatrick 1975). However, as evidenced by only minor changes (*5%) in heat there is an increase in surface energy associated with capacity across the glass transition (Neuville et al. 1993). breaking the spherical symmetry of a growing spherulite. Hence, there is no reason to believe that the glass transition The stability of a spherical interface with finite surface represents an abrupt barrier to spherulite growth. However, tension is determined by a competition between growth it is apparent from the diffusion-controlled growth model rate and diffusion rate. At low growth rates, surface tension that growth rates become prohibitively slow below about and diffusion act to maintain a minimum surface energy 400°C. configuration (i.e., spherical). With increasing growth rate, however, there comes a critical point described by the Why doesn’t spherulite growth lead to runaway Mullins–Sekerka instability at which diffusion and surface heating? tension can no longer prohibit dendritic growth (Mullins and Sekerka 1963; Langer 1980). As one might expect, the An issue we have not yet addressed is the release and transition from spherical to dendritic morphology depends transport of latent heat as spherulitic crystallization pro- on the diffusion length over which the crystallizing com- gresses (cf. Lofgren 1971a). Diffusion of latent heat into ponents are depleted. Qualitatively, for large diffusion the surrounding matrix could insulate growing spherulites, lengths the increase in supersaturation surrounding a pro- prolonging their exposure to elevated temperatures. Latent trusion is minor compared to the rest of the spherulite. In heat could also, in principle, lead to increased growth rates this regard, we attribute the sphericity of spherulites in our and the release of more latent heat in a positive feedback samples to the high mobility of water (in relation to reac- loop (Carmichael, personal communication). Obviously, tion kinetics) throughout their growth history. this runaway heating does not take place since almost all spherulite-bearing rocks are vitrophyric. In order to explain this, we again turn to diffusion-controlled growth. We have Conclusions already shown that spherulite growth is limited by the mobility of chemical species, and that spherulite growth Water concentration profiles adjacent to spherulite rims rates proceed on the same timescale as water diffusion provide information about the growth history of spherulites -6 2 rates. A maximum DOH of about 10 mm /s in rhyolite in rhyolitic vitrophyres. We have shown that these profiles corresponds to T = 850°C. This is seven orders of magni- can be modeled assuming a combination of diffusion- tude lower than thermal diffusivity in obsidian, which is on controlled spherulite growth kinetics and post-growth dif- the order of 10-1 mm2/s over the temperature range 0– fusion of water. Qualitatively, this model can resolve 800°C (Riehle et al. 1995). Hence, latent heat is carried temperature differences at which different spherulites grew away long before it can influence spherulite growth rates. and it accounts for why spherulites are spherical. We find that the glass transition is not a barrier to spherulite growth Why are spherulites spherical? because chemical diffusivities are not sensitive to this transition. Furthermore, because thermal diffusivities are Natural spherulites are host to multiple crystalline phases much faster than chemical diffusivities, spherulite crystal- with very different individual morphologies (Fig. 1). On lization does not lead to runaway heating and complete the whole, however, spherulites are almost perfectly crystallization or devitrification of rhyolitic vitrophyres. spherical. The simplest explanation is that their host glass Our model also provides timescales for spherulite or melt is homogeneous, thus offering no preferred direc- growth. Swanson (1977) was the first to show that crystals tion in which to grow. As we noted earlier, however, some can grow to large sizes (mm-scale) on surprisingly short spherulites cross cut bands of textural and compositional timescales (on the order of days) in systems with more than heterogeneities (Gonnermann and Manga 2003). An alter- one phase. We have inferred that this holds true in the native explanation can be found by invoking sufficiently natural setting where spherulites can grow to large sizes on rapid diffusion of water. the order of days at eruptive temperatures. However, As spherulites grow outwards and water is rejected into spherulite growth rates decrease exponentially with tem- the surrounding matrix, there is a local reduction in the perature and become prohibitively slow at temperatures relative abundance of crystal-forming components. Since below about 400°C. water content decreases with distance (over diffusion Lastly, we emphasize that the results presented here are lengthscales) from the spherulite rim, any crystalline pro- based on spherulites from a single locality. A similar trusion will grow into a melt at a higher supersaturation approach applied to spherulites from elsewhere will be 123 Contrib Mineral Petrol useful in the future. In particular, we would like to compare Kirkpatrick R (1975) Crystal growth from the melt: a review. Am timescales of during- and post-growth diffusion of water Mineral 60(9–10):798–814 Langer J (1980) Instabilities and pattern formation in crystal growth. between spherulites that experienced different cooling Rev Mod Phys 52:1–27 histories. Information such as this may lead to an expla- Lewis-Kenedi C, Lange R, Hall C, Delgado-Grenados H (2005) The nation for how and when spherulite growth and water eruptive history of the Tequila volcanic field, western Mexico: diffusion become decoupled. ages, volumes, and relative proportions of lava types. Bull Volcanol 67:391–414 Lofgren G (1971a) Spherulitic textures in glassy and crystalline rocks. Acknowledgments We would like to thank Ian Carmichael for J Geophys Res 76:5635–5648 providing samples and suggesting that spherulites were interesting Lofgren G (1971b) Experimentally produced devitrification textures and important. We also thank the Advanced Light Source and Kent in natural rhyolite glass. 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